Question

determinati numerele a si b stiinde ca:a)raportul lor este 3/7 iar suma lor este 120.
b)raportul lor este 3/4 iar 2a+3b=90
c)a/5=b/7iar a+b=24
d)b/4=a/5 si 3b+4a=96
e)a/7=b/3 si a-b=48
f)a/9=b/7 si 2a+b=75

Answer 1

a) a/b = 3/7 --> a = 3b/7

a+b = 120
3b/7+b = 120
3b+7b = 840
10b = 840
b = 84.

a = 3b/7
a = 252/7
a = 36.


Verificare : a+b = 36+84 = 120.



b) a/b = 3/4 --> a = 3b/4

2a+3b = 90
2•3b/4+3b = 90
3b/2+3b = 90
3b+6b = 180
9b = 180
b = 20.

a = 3b/4
a = 3•20/4
a = 3•5
a = 15.


Verificare : 2a+3b = 2•15+3•20 = 30+60 = 90.



c) a/5 = b/7 --> a = 5b/7

a+b = 24
5b/7+b = 24
5b+7b = 168
12b = 168
b = 14.

a = 5b/7
a = 5•14/7
a = 5•2
a = 10.

Verificare : a+b = 10+14 = 24.



d) b/4 = a/5 --> b = 4a/5

3b+4a = 96
3•4a/5+4a = 96
12a/5+4a = 96
12a+20a = 480
32a = 480
a = 15.

b = 4a/5
b = 4•15/5
b = 4•3
b = 12.


Verificare : 3b+4a = 3•12+4•15 = 36+60 = 96.



e) a/7 = b/3 --> a = 7b/3

a-b = 48
7b/3-b = 48
7b-3b = 144
4b = 144
b = 36.

a = 7b/3
a = 7•36/3
a = 7•12
a = 84.


Verificare : a-b = 84-36 = 48.


f) a/9 = b/7 --> a = 9b/7

2a+b = 75
2•9b/7+b = 75
18b/7+b = 75
18b+7b = 525
25b = 525
b = 21.

a = 9b/7
a = 9•21/7
a = 9•3
a = 27.


Verificare : 2a+b = 2•27+21 = 54+21 = 75.




J'espère aidé :)